The function \(u^+\)  is typically concave on gains, while \(-u^-\)  is typically convex on losses [1]}.
The distortion of extremely low and extremely high probability events by humans can be represented by a weight function that takes an inverted S-shape- i.e., it is concave for small probabilities, and convex for large probabilities (e.g., \(w(\kappa )= \exp (-(-\ln \kappa )^\eta ), 0 < \eta < 1\) ) [1]}, [3]}.
The CPT-value generalizes other risk metrics
for appropriate choices of weighting functions.
For example, when \(w^+, w^-\)  are identity functions, and \(u^+(x) = x, x \ge 0\) , \(u^-(x) = -x, x \le 0\) , we obtain \(\rho _{cpt}(Y) = \mathbb {E}[Y]\) .
